

A328176


a(n) is the maximal value of the expression d AND (n/d) where d runs through the divisors of n and AND denotes the bitwise AND operator.


3



1, 0, 1, 2, 1, 2, 1, 0, 3, 0, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 3, 2, 1, 4, 5, 0, 1, 4, 1, 4, 1, 0, 3, 0, 5, 6, 1, 2, 1, 0, 1, 6, 1, 2, 3, 2, 1, 4, 7, 0, 1, 4, 1, 2, 1, 4, 3, 0, 1, 4, 1, 2, 1, 8, 5, 2, 1, 2, 3, 4, 1, 8, 1, 0, 5, 2, 3, 4, 1, 8, 9, 0, 1, 6, 1, 2, 1
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OFFSET

1,4


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..16384
Rémy Sigrist, Scatterplot of the first 2^16 terms


FORMULA

a(n)^2 <= n with equality iff n is a square.
a(n) = 1 for any odd prime number p.
a(n) <= A327987(n).
a(n) = 0 iff n belongs to A327988.


EXAMPLE

For n = 12:
 we have the following values:
d 12/d d AND (12/d)
  
1 12 0
2 6 2
3 4 0
4 3 0
6 2 2
12 1 0
 hence a(12) = max({0, 2}) = 2.


MAPLE

a:= n> max(map(d> Bits[And](d, n/d), numtheory[divisors](n))):
seq(a(n), n=1..100); # Alois P. Heinz, Oct 09 2019


PROG

(PARI) a(n) = vecmax(apply(d > bitand(d, n/d), divisors(n)))


CROSSREFS

See A328177 and A328178 for similar sequences.
Cf. A327987, A327988.
Sequence in context: A030205 A159817 A079532 * A191312 A240159 A309447
Adjacent sequences: A328173 A328174 A328175 * A328177 A328178 A328179


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Oct 06 2019


STATUS

approved



